Mixed Marginal Copula Modeling

TL;DR

This paper develops a Bayesian framework for copula models with mixed discrete and continuous marginals, enabling flexible modeling of complex dependencies in multivariate data.

Contribution

It introduces a general likelihood definition for mixed marginals and applies Bayesian MCMC methods to estimate such models, focusing on Gaussian and Archimedean copulas.

Findings

Effective estimation of mixed marginal copulas demonstrated

Application to income dynamics shows practical utility

Framework extends copula modeling capabilities

Abstract

This article extends the literature on copulas with discrete or continuous marginals to the case where some of the marginals are a mixture of discrete and continuous components. We do so by carefully defining the likelihood as the density of the observations with respect to a mixed measure. The treatment is quite general, although we focus focus on mixtures of Gaussian and Archimedean copulas. The inference is Bayesian with the estimation carried out by Markov chain Monte Carlo. We illustrate the methodology and algorithms by applying them to estimate a multivariate income dynamics model.